SOLUTION: Which of the following equations represents a line l that goes through (–2, 3) and has a slope of –4? A) y = –4x – 1 B) y = –4x – 5 C) y = –4x + 5 D) y = –4x + 1

Algebra ->  Graphs -> SOLUTION: Which of the following equations represents a line l that goes through (–2, 3) and has a slope of –4? A) y = –4x – 1 B) y = –4x – 5 C) y = –4x + 5 D) y = –4x + 1      Log On


   

Question 150042: Which of the following equations represents a line l that goes through (–2, 3) and has a slope of –4?
A) y = –4x – 1
B) y = –4x – 5
C) y = –4x + 5
D) y = –4x + 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of -4 which goes through the point (-2,3), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-3=%28-4%29%28x--2%29 Plug in m=-4, x%5B1%5D=-2, and y%5B1%5D=3 (these values are given)


y-3=%28-4%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-3=-4x%2B%28-4%29%282%29 Distribute -4

y-3=-4x-8 Multiply -4 and 2 to get -8

y=-4x-8%2B3 Add 3 to both sides to isolate y

y=-4x-5 Combine like terms -8 and 3 to get -5
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Answer:


So the equation of the line with a slope of -4 which goes through the point (-2,3) is:

y=-4x-5 which is now in y=mx%2Bb form where the slope is m=-4 and the y-intercept is b=-5

Notice if we graph the equation y=-4x-5 and plot the point (-2,3), we get (note: if you need help with graphing, check out this solver)

Graph of y=-4x-5 through the point (-2,3)
and we can see that the point lies on the line. Since we know the equation has a slope of -4 and goes through the point (-2,3), this verifies our answer.